Spontaneous symmetry-breaking in equilibrium tree-packing configurations of a kinetically constrained cubic-lattice system

What the math gives to ML

The paper provides a nonstandard constrained-configuration mechanism: configurations reachable under the Fredrikson–Andersen kinetic rule with K=2 form occupied-site forests, and their equilibrium partition function exhibits a continuous gas–crystal transition with spontaneous selection of one of two cubic sublattices at chemical potential \(\mu^*\approx-3.252\). This can be transferred to structured neural sparsity by treating active connections or computational units as occupied sites and restricting the active interaction graph to be loop-free, limiting redundant feedback paths while preserving tree-like information flow. The key experimentally testable asset is a controllable symmetry-breaking transition: sweeping a sparsity chemical potential should produce a sharp increase in sublattice imbalance and a corresponding change in optimization or inference behavior.